I doubt that Europeans are making healthier choices primarily from a bigger focus on education around food. I think they come across as better educated because they grew up with laws that encouraged certain food systems. I'd imagine they'd have an easier time naming the ingredients of the bread they eat than Americans could, due to laws. I think the education starts with the politics of the food system.

I think food deserts play a role, but the biggest suspicion I have is partly how much time and energy winds up devoted to work. While it's nothing compared to say Japan or Korea, it remains common to dedicate 10+ hours of the day to work and related tasks. With what's left people often go for quick and easy options like takeout and frozen food. Poorer people also are more likely to have to work longer hours in addition to living in food deserts and having less access to reliable transportation.

But also our food culture changed radically in the 20th century. We were a young country, with a young culture when industrialization hit. When food production changed we got all on board. That recipe that's been in your family for generations is more likely to come from the Campbell corporation than the old country. And from there a lot of families since WWII didn't really teach their kids to cook. Maybe they taught a little, but the American monoculture's idea of foods is so generational that there isn't the sort of continuity Europeans have outside stuff like regional poverty foods (where every ingredient comes from a can). Frozen foods became extremely popular as women reentered the workforce in the 70s, and this became a huge part of American culinary habit with the famous "TV dinner"

Then we can talk subsidies. In the 1930s we passed a massive collection of governmental and economic reforms to deal with the great depression called the new deal. Among those reforms was massive subsidies to farming intended to prevent a repeat of the overfarming of the topsoil in our primary grain producing region as well as to ensure that small farmers wouldn't keep going bust. This ultimately resulted in us producing a metric fuckton of maize. To the point where if maize can do something, the only way it isn't the cheapest option is if petroleum or soy can do it similarly well. We have cheap cane sugar thanks to Florida and Hawaii, but hfcs is dirt cheap. These farming subsidies also are why low quality, standardized cheese is in everything here. Our government purchases dairy to keep it profitable to produce, makes generic mass produced cheeses with it to ensure it keeps, then sells it off en masse. Our government invented the cheese stuffed crust pizza to keep our dairy farmers afloat, same for every other fast food meal with too much cheese.

Do y'all learn to cook in school? Also yeah, some of us are lazier or less willing to spend limited energy cooking. I personally am rare in that most of my dinners are homemade. But I feel ascribing any cultural trend or trait to laziness is more easy than useful.